An extension of lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems

Guisheng Zhai; Xuping Xu; Hai Lin; Derong Liu

An extension of lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems

Guisheng Zhai, Xuping Xu, Hai Lin, Derong Liu

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show that there is a common quadratic Lyapunov-like function for all subsystems and the switched system is exponentially stable under a dwell time scheme. Two numerical examples are provided to demonstrate the result.

Original language	English
Title of host publication	Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06
Pages	362-367
Number of pages	6
Publication status	Published - 2006
Externally published	Yes
Event	2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06 - Ft. Lauderdale, FL, United States Duration: 2006 Apr 23 → 2006 Apr 25

Publication series

Name	Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06

Conference

Conference	2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06
Country/Territory	United States
City	Ft. Lauderdale, FL
Period	06/4/23 → 06/4/25

Keywords

Arbitrary switching
Common quadratic lyapunov (lyapunov-iike) functions
Dwell time scheme
Exponential stability
Lie algebra
Switched systems

ASJC Scopus subject areas

Computer Networks and Communications
Control and Systems Engineering

Cite this

Zhai, G., Xu, X., Lin, H., & Liu, D. (2006). An extension of lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems. In Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06 (pp. 362-367). [1673173] (Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06).

An extension of lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems. / Zhai, Guisheng; Xu, Xuping; Lin, Hai et al.
Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06. 2006. p. 362-367 1673173 (Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Zhai, G, Xu, X, Lin, H & Liu, D 2006, An extension of lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems. in Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06., 1673173, Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06, pp. 362-367, 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06, Ft. Lauderdale, FL, United States, 06/4/23.

Zhai G, Xu X, Lin H, Liu D. An extension of lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems. In Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06. 2006. p. 362-367. 1673173. (Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06).

Zhai, Guisheng ; Xu, Xuping ; Lin, Hai et al. / An extension of lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems. Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06. 2006. pp. 362-367 (Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06).

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abstract = "We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show that there is a common quadratic Lyapunov-like function for all subsystems and the switched system is exponentially stable under a dwell time scheme. Two numerical examples are provided to demonstrate the result.",

keywords = "Arbitrary switching, Common quadratic lyapunov (lyapunov-iike) functions, Dwell time scheme, Exponential stability, Lie algebra, Switched systems",

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Y1 - 2006

N2 - We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show that there is a common quadratic Lyapunov-like function for all subsystems and the switched system is exponentially stable under a dwell time scheme. Two numerical examples are provided to demonstrate the result.

AB - We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show that there is a common quadratic Lyapunov-like function for all subsystems and the switched system is exponentially stable under a dwell time scheme. Two numerical examples are provided to demonstrate the result.

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KW - Common quadratic lyapunov (lyapunov-iike) functions

KW - Dwell time scheme

KW - Exponential stability

KW - Lie algebra

KW - Switched systems

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An extension of lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

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